What Andar said is correct, the game engine searches for mp/hp/tp by default, while using a new name for each is possible, it still require us to point it back to either hp/mp/tp to work. To add a brand new category will means we need to tinker with the damage formulas/action class and more. And will pretty much ended up with LOTS of tags(to do formula calculations) for each skill/item/class/actor/enemy.
While it sound simple on the scripting part, to make it flexible and works for a 3rd party user, the game making part for those users will turn out to be stressing and confusing.
And what you want sounds like the default TP to me.
Just rename the TP to MP in the editor's database if you are not using it and use is as MP for your other characters.
Then in the character page, you should be able to set the "recovering %" of TP there for the actor you want to recover over time(steps actually).
Next, add gain tp to all the skill the actor you want to heal tp when they attack.
and finally the last one require you to do a if
formula in all the enemy's attack skill. if actor X is the target, heal his/her tp.
Max TP can be changed under
Game_BattlerBase
look for the line: def max_tp
and change 100 to whatever you like.